MeLOn
Train_GP_and_return_hyperparameters.m File Reference

Functions

id OptGP ()
 
id Xnew ()
 
hypVar, Xnew, Ynew, K_M, Opt.GP NLikelihood ()
 
see Jones paper lb (h1+h2)
 
 ub (h1+h2)
 
Xnew size ()
 
 warning ('Covariance matrix in Nlikelihood is not positive semi-definite') end % invK = 2*sum(log(abs(diag(CH))))
 
dNLL_f cov (i)
 
dNLL_f lik (i)
 
id nSpectralpoints ()
 
Posterior sample (function) according to theta f
 
return function Yi Cao All rights reserved Redistribution and use in source and binary with or without are permitted provided that the following conditions are this list of conditions and the following disclaimer *Redistributions in binary form must reproduce the above copyright this list of conditions and the following disclaimer in the documentation and or other materials provided with the distribution THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED BUT NOT LIMITED THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF % SUBSTITUTE GOODS OR SERVICES;LOSS OF USE, DATA, OR PROFITS;OR BUSINESS % INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY
 
return function Yi Cao All rights reserved Redistribution and use in source and binary with or without are permitted provided that the following conditions are this list of conditions and the following disclaimer *Redistributions in binary form must reproduce the above copyright this list of conditions and the following disclaimer in the documentation and or other materials provided with the distribution THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED BUT NOT LIMITED THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY OR CONSEQUENTIAL WHETHER IN STRICT OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) % ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE
 
 error (nargoutchk(0, 1, nargout))
 

Variables

file Train_GP_and_return_hyperparameters m brief Trains a Gaussian processe and returns hyperparameters
 
file Train_GP_and_return_hyperparameters m brief Trains a Gaussian processe and returns RWTH Aachen University n
 
file Train_GP_and_return_hyperparameters m brief Trains a Gaussian processe and returns RWTH Aachen University Xiaopeng Lin
 
file Train_GP_and_return_hyperparameters m brief Trains a Gaussian processe and returns RWTH Aachen University Xiaopeng Daniel Grothe
 
file Train_GP_and_return_hyperparameters m brief Trains a Gaussian processe and returns RWTH Aachen University Xiaopeng Daniel and Alexander Mitsos date January function [Opt]
 
Scale Variables [xScaled, yScaled] = ScaleVariables(X,Y,lb,ub)
 
Training of GP for j
 
end Calculate covariance matrix and inverse of covariance matrix for i
 
end return Artur M Schweidtmann and Alexei Lapkin
 
Set initial hyperparameters h1 = Opt.GP.h1
 
number of hyperparameters from covariance h2 = Opt.GP.h2
 
 K_M = zeros(n,n*D)
 
Define bounds lb = ones(h1+h2,1) * log(sqrt(10^(-3)))
 
see Jones paper ub = ones(h1+h2,1) * log(sqrt(10^(3)))
 
 bounds = [lb,ub]
 
opts maxevals = Opt.GP.fun_eval*(h1+h2)
 
opts maxits = 100000*(h1+h2)
 
opts maxdeep = 100000*(h1+h2)
 
opts showits = 0
 
Defintion of options for global search [~, x0] = Direct(obj_fun,bounds,opts)
 
Defintion of options for fmincon solver LSoptions Algorithm = 'interior-point'
 
LSoptions DerivativeCheck = 'off'
 
LSoptions TolCon = 1e-12
 
LSoptions Display = 'off'
 
LSoptions Hessian = 'bfgs'
 
LSoptions TolFun = 1e-12
 
LSoptions PlotFcns = []
 
LSoptions GradConstr = 'off'
 
LSoptions GradObj = 'on'
 
LSoptions TolX = 1e-14
 
LSoptions UseParallel = 0
 
Solve optimization problem hypResult = fmincon(obj_fun.f,x0,[],[],[],[],lb,ub,[],LSoptions)
 
Return optimal hyperparameters Opt GP hyp cov = hypResult(1:h1)
 
Opt GP hyp lik = hypResult(h1+1:h1+h2)
 
 OptGPhyp = Opt.GP.hyp
 
Opt GP = OptGP
 
type of Martern else d = 1
 
number of hyperparameters from likelihood hyp = Opt.GP.hyp
 
 ell = exp(hyp.cov(1:D))
 
 sf2 = exp(2*hyp.cov(D+1))
 
 K = zeros(n,n)
 
 expnK = exp(-sqrtK)
 
 sqrtK = []
 
end if Opt GP t = sqrtK
 
 m = (1 + t).*expnK
 
This guarantees a symmetric matrix Calculate inverse of covariance matrix try CH = chol(K)
 
 invK = CH\(CH'\eye(n))
 
Calculate hyperperpriors logprior = 0
 
 dlogpriorcov = zeros(1,h1)
 
end dlogpriorlik = zeros(1,h2)
 
Gradient calculation if nargout
 
end c = invK*Ynew
 
 b = invK* dK
 
end dNLL = [dNLL_f.cov'
 
end return function f
 
 sn2 = exp(2*Opt.hyp.lik)
 
else W = randn(nSpectralpoints,D) .* repmat(1./ell', nSpectralpoints, 1)
 
Calculation of phi phi = sqrt(2 * sf2 / nSpectralpoints) * cos(W * Xnew' + repmat(b, 1, n))
 
Sampling of theta according to phi A = phi * phi' + sn2 * eye(nSpectralpoints)
 
 invA = invChol(A)
 
 mu_theta = invA*phi*Ynew
 
 cov_theta = sn2*invA
 
 theta = mvnrnd(mu_theta,cov_theta)'
 
return function v
 
return function Yi Cao All rights reserved Redistribution and use in source and binary forms
 
return function Yi Cao All rights reserved Redistribution and use in source and binary with or without modification
 
return function Yi Cao All rights reserved Redistribution and use in source and binary with or without are permitted provided that the following conditions are met
 
return function Yi Cao All rights reserved Redistribution and use in source and binary with or without are permitted provided that the following conditions are this list of conditions and the following disclaimer *Redistributions in binary form must reproduce the above copyright notice
 
return function Yi Cao All rights reserved Redistribution and use in source and binary with or without are permitted provided that the following conditions are this list of conditions and the following disclaimer *Redistributions in binary form must reproduce the above copyright this list of conditions and the following disclaimer in the documentation and or other materials provided with the distribution THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED WARRANTIES
 
return function Yi Cao All rights reserved Redistribution and use in source and binary with or without are permitted provided that the following conditions are this list of conditions and the following disclaimer *Redistributions in binary form must reproduce the above copyright this list of conditions and the following disclaimer in the documentation and or other materials provided with the distribution THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED INCLUDING
 
return function Yi Cao All rights reserved Redistribution and use in source and binary with or without are permitted provided that the following conditions are this list of conditions and the following disclaimer *Redistributions in binary form must reproduce the above copyright this list of conditions and the following disclaimer in the documentation and or other materials provided with the distribution THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED BUT NOT LIMITED TO
 
return function Yi Cao All rights reserved Redistribution and use in source and binary with or without are permitted provided that the following conditions are this list of conditions and the following disclaimer *Redistributions in binary form must reproduce the above copyright this list of conditions and the following disclaimer in the documentation and or other materials provided with the distribution THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED BUT NOT LIMITED THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT
 
return function Yi Cao All rights reserved Redistribution and use in source and binary with or without are permitted provided that the following conditions are this list of conditions and the following disclaimer *Redistributions in binary form must reproduce the above copyright this list of conditions and the following disclaimer in the documentation and or other materials provided with the distribution THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED BUT NOT LIMITED THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY INDIRECT
 
return function Yi Cao All rights reserved Redistribution and use in source and binary with or without are permitted provided that the following conditions are this list of conditions and the following disclaimer *Redistributions in binary form must reproduce the above copyright this list of conditions and the following disclaimer in the documentation and or other materials provided with the distribution THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED BUT NOT LIMITED THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY INCIDENTAL
 
return function Yi Cao All rights reserved Redistribution and use in source and binary with or without are permitted provided that the following conditions are this list of conditions and the following disclaimer *Redistributions in binary form must reproduce the above copyright this list of conditions and the following disclaimer in the documentation and or other materials provided with the distribution THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED BUT NOT LIMITED THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY SPECIAL
 
return function Yi Cao All rights reserved Redistribution and use in source and binary with or without are permitted provided that the following conditions are this list of conditions and the following disclaimer *Redistributions in binary form must reproduce the above copyright this list of conditions and the following disclaimer in the documentation and or other materials provided with the distribution THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED BUT NOT LIMITED THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY EXEMPLARY
 
return function Yi Cao All rights reserved Redistribution and use in source and binary with or without are permitted provided that the following conditions are this list of conditions and the following disclaimer *Redistributions in binary form must reproduce the above copyright this list of conditions and the following disclaimer in the documentation and or other materials provided with the distribution THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED BUT NOT LIMITED THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY OR CONSEQUENTIAL WHETHER IN CONTRACT
 
return function Yi Cao All rights reserved Redistribution and use in source and binary with or without are permitted provided that the following conditions are this list of conditions and the following disclaimer *Redistributions in binary form must reproduce the above copyright this list of conditions and the following disclaimer in the documentation and or other materials provided with the distribution THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED BUT NOT LIMITED THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY OR CONSEQUENTIAL WHETHER IN STRICT LIABILITY
 
return function Yi Cao All rights reserved Redistribution and use in source and binary with or without are permitted provided that the following conditions are this list of conditions and the following disclaimer *Redistributions in binary form must reproduce the above copyright this list of conditions and the following disclaimer in the documentation and or other materials provided with the distribution THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED BUT NOT LIMITED THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY OR CONSEQUENTIAL WHETHER IN STRICT OR EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE HYPERVOUME Hypervolume indicator as a measure of Pareto front estimate V
 
return function Yi Cao All rights reserved Redistribution and use in source and binary with or without are permitted provided that the following conditions are this list of conditions and the following disclaimer *Redistributions in binary form must reproduce the above copyright this list of conditions and the following disclaimer in the documentation and or other materials provided with the distribution THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED BUT NOT LIMITED THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY OR CONSEQUENTIAL WHETHER IN STRICT OR EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE HYPERVOUME Hypervolume indicator as a measure of Pareto front estimate paretoGroup Version by Yi Cao at Cranfield University on April Example
 
upper bound of the data set r =max(F)
 
Approximation of Pareto set P =paretofront(F)
 
https __pad0__
 
https nargin
 

Function Documentation

◆ cov()

dNLL_f cov ( i  )

◆ DAMAGES()

return function Yi Cao All rights reserved Redistribution and use in source and binary with or without are permitted provided that the following conditions are this list of conditions and the following disclaimer* Redistributions in binary form must reproduce the above copyright this list of conditions and the following disclaimer in the documentation and or other materials provided with the distribution THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED BUT NOT LIMITED THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY OR CONSEQUENTIAL DAMAGES ( INCLUDING  ,
BUT NOT LIMITED  TO,
PROCUREMENT OF % SUBSTITUTE GOODS OR SERVICES;LOSS OF  USE,
DATA  ,
OR PROFITS;OR BUSINESS %  INTERRUPTION 
)

◆ error()

error ( nargoutchk(0, 1, nargout )

◆ lb()

see Jones paper lb ( h1 h2)

◆ lik()

dNLL_f lik ( i  )

◆ NLikelihood()

hypVar,Xnew,Ynew,K_M,Opt.GP NLikelihood ( )
virtual

◆ nSpectralpoints()

id nSpectralpoints ( )
virtual

◆ OptGP()

id OptGP ( )
virtual

◆ sample()

Posterior sample ( function  )

◆ size()

Xnew size ( )
virtual

◆ TORT()

return function Yi Cao All rights reserved Redistribution and use in source and binary with or without are permitted provided that the following conditions are this list of conditions and the following disclaimer* Redistributions in binary form must reproduce the above copyright this list of conditions and the following disclaimer in the documentation and or other materials provided with the distribution THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED BUT NOT LIMITED THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY OR CONSEQUENTIAL WHETHER IN STRICT OR TORT ( INCLUDING NEGLIGENCE OR  OTHERWISE)

◆ ub()

ub ( h1 h2)

◆ warning()

warning ( 'Covariance matrix in Nlikelihood is not positive semi-definite'  ) = 2*sum(log(abs(diag(CH))))

◆ Xnew()

id Xnew ( )
virtual

Variable Documentation

◆ __pad0__

https __pad0__

◆ A

Sampling of theta according to phi A = phi * phi' + sn2 * eye(nSpectralpoints)

◆ Algorithm

Defintion of options for fmincon solver LSoptions Algorithm = 'interior-point'

◆ b

end b = invK* dK

◆ bounds

bounds = [lb,ub]

◆ c

end c = invK*Ynew

◆ CH

catch CH = chol(K)

◆ CONTRACT

return function Yi Cao All rights reserved Redistribution and use in source and binary with or without are permitted provided that the following conditions are this list of conditions and the following disclaimer* Redistributions in binary form must reproduce the above copyright this list of conditions and the following disclaimer in the documentation and or other materials provided with the distribution THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED BUT NOT LIMITED THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY OR CONSEQUENTIAL WHETHER IN CONTRACT

◆ cov

Sampling of W and b if Opt cov = hypResult(1:h1)

◆ cov_theta

cov_theta = sn2*invA

◆ d

type of Martern else d = 1

◆ DerivativeCheck

LSoptions DerivativeCheck = 'off'

◆ DIRECT

return function Yi Cao All rights reserved Redistribution and use in source and binary with or without are permitted provided that the following conditions are this list of conditions and the following disclaimer* Redistributions in binary form must reproduce the above copyright this list of conditions and the following disclaimer in the documentation and or other materials provided with the distribution THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED BUT NOT LIMITED THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT

◆ Display

LSoptions Display = 'off'

◆ dlogpriorcov

id dlogpriorcov = zeros(1,h1)

◆ dlogpriorlik

dlogpriorlik = zeros(1,h2)

◆ dNLL

end dNLL = [dNLL_f.cov'

◆ ell

ell = exp(hyp.cov(1:D))

◆ Example

return function Yi Cao All rights reserved Redistribution and use in source and binary with or without are permitted provided that the following conditions are this list of conditions and the following disclaimer* Redistributions in binary form must reproduce the above copyright this list of conditions and the following disclaimer in the documentation and or other materials provided with the distribution THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED BUT NOT LIMITED THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY OR CONSEQUENTIAL WHETHER IN STRICT OR EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE HYPERVOUME Hypervolume indicator as a measure of Pareto front estimate paretoGroup Version by Yi Cao at Cranfield University on April Example
Initial value:
{
% an random exmaple
F=(randn(100,3)+5).^2

◆ EXEMPLARY

return function Yi Cao All rights reserved Redistribution and use in source and binary with or without are permitted provided that the following conditions are this list of conditions and the following disclaimer* Redistributions in binary form must reproduce the above copyright this list of conditions and the following disclaimer in the documentation and or other materials provided with the distribution THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED BUT NOT LIMITED THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY EXEMPLARY

◆ expnK

else expnK = exp(-sqrtK)

◆ f

end return function f
Initial value:
= posterior_sample(Xnew,Ynew,Opt)
% Copyright (c) by Eric Bradford

◆ forms

return function Yi Cao All rights reserved Redistribution and use in source and binary forms

◆ function

return function[NLL, dNLL]
Initial value:
= Train_GP_and_return_hyperparameters(X,Y,lb,ub,Opt)
%% Set up options
Opt = set_option_structure(Opt,X,Y)

◆ GP

Opt GP = OptGP

◆ GradConstr

LSoptions GradConstr = 'off'

◆ GradObj

LSoptions GradObj = 'on'

◆ Grothe

file Train_GP_and_return_hyperparameters m brief Trains a Gaussian processe and returns RWTH Aachen University Xiaopeng Daniel Grothe

◆ h1

end h1 = Opt.GP.h1

◆ h2

number of hyperparameters from covariance h2 = Opt.GP.h2

◆ Hessian

LSoptions Hessian = 'bfgs'

◆ hyp

number of hyperparameters from likelihood hyp = Opt.GP.hyp

◆ hyperparameters

file Train_GP_and_return_hyperparameters m brief Trains a Gaussian processe and returns hyperparameters
Initial value:
==============================================================================\n
% Aachener Verfahrenstechnik-Systemverfahrenstechnik

◆ hypResult

Solve optimization problem hypResult = fmincon(obj_fun.f,x0,[],[],[],[],lb,ub,[],LSoptions)

◆ i

end for i
Initial value:
= 1:Opt.Gen.NoOfGPs
[Opt.GP(i).K,Opt.GP(i).invK] = CalcCovMatrix(xScaled, Opt.GP(i))

◆ INCIDENTAL

return function Yi Cao All rights reserved Redistribution and use in source and binary with or without are permitted provided that the following conditions are this list of conditions and the following disclaimer* Redistributions in binary form must reproduce the above copyright this list of conditions and the following disclaimer in the documentation and or other materials provided with the distribution THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED BUT NOT LIMITED THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY INCIDENTAL

◆ INCLUDING

return function Yi Cao All rights reserved Redistribution and use in source and binary with or without are permitted provided that the following conditions are this list of conditions and the following disclaimer* Redistributions in binary form must reproduce the above copyright this list of conditions and the following disclaimer in the documentation and or other materials provided with the distribution THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED INCLUDING

◆ INDIRECT

return function Yi Cao All rights reserved Redistribution and use in source and binary with or without are permitted provided that the following conditions are this list of conditions and the following disclaimer* Redistributions in binary form must reproduce the above copyright this list of conditions and the following disclaimer in the documentation and or other materials provided with the distribution THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED BUT NOT LIMITED THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY INDIRECT

◆ invA

invA = invChol(A)

◆ invK

invK = CH\(CH'\eye(n))

◆ j

for j
Initial value:
= 1:Opt.Gen.NoOfGPs
[Opt.GP(j).hyp] = TrainingOfGP(xScaled,yScaled(:,j),Opt.GP(j))

◆ K

K = zeros(n,n)

◆ K_M

K_M = zeros(n,n*D)

◆ Lapkin

end return function Artur M Schweidtmann and Alexei Lapkin

◆ lb

Define bounds lb = ones(h1+h2,1) * log(sqrt(10^(-3)))

◆ LIABILITY

return function Yi Cao All rights reserved Redistribution and use in source and binary with or without are permitted provided that the following conditions are this list of conditions and the following disclaimer* Redistributions in binary form must reproduce the above copyright this list of conditions and the following disclaimer in the documentation and or other materials provided with the distribution THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED BUT NOT LIMITED THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY OR CONSEQUENTIAL WHETHER IN STRICT LIABILITY

◆ lik

hyp lik = hypResult(h1+1:h1+h2)

◆ Lin

file Train_GP_and_return_hyperparameters m brief Trains a Gaussian processe and returns RWTH Aachen University Xiaopeng Lin

◆ logprior

*pi logprior = 0

◆ m

elseif Opt GP m = (1 + t).*expnK

◆ maxdeep

opts maxdeep = 100000*(h1+h2)

◆ maxevals

opts maxevals = Opt.GP.fun_eval*(h1+h2)

◆ maxits

opts maxits = 100000*(h1+h2)

◆ met

return function Yi Cao All rights reserved Redistribution and use in source and binary with or without are permitted provided that the following conditions are met

◆ modification

return function Yi Cao All rights reserved Redistribution and use in source and binary with or without modification

◆ mu_theta

mu_theta = invA*phi*Ynew

◆ n

file Train_GP_and_return_hyperparameters m brief Trains a Gaussian processe and returns RWTH Aachen University n
Initial value:
==============================================================================\n
%
% @author Artur Schweidtmann

◆ nargin

https nargin

◆ nargout

Gradient calculation if nargout
Initial value:
== 2 % do only if No of output variable is 2 (if necessary)
dsq_M = zeros(n,n*D)

◆ notice

return function Yi Cao All rights reserved Redistribution and use in source and binary with or without are permitted provided that the following conditions are this list of conditions and the following disclaimer* Redistributions in binary form must reproduce the above copyright notice

◆ OptGPhyp

OptGPhyp = Opt.GP.hyp

◆ P

P =paretofront(F)

◆ phi

Calculation of phi phi = sqrt(2 * sf2 / nSpectralpoints) * cos(W * Xnew' + repmat(b, 1, n))

◆ PlotFcns

LSoptions PlotFcns = []

◆ r

upper bound of the data set r =max(F)

◆ search

Defintion of options for global search[~, x0] = Direct(obj_fun,bounds,opts)

◆ sf2

sf2 = exp(2*hyp.cov(D+1))

◆ showits

opts showits = 0

◆ sn2

sn2 = exp(2*Opt.hyp.lik)

◆ SPECIAL

return function Yi Cao All rights reserved Redistribution and use in source and binary with or without are permitted provided that the following conditions are this list of conditions and the following disclaimer* Redistributions in binary form must reproduce the above copyright this list of conditions and the following disclaimer in the documentation and or other materials provided with the distribution THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED BUT NOT LIMITED THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY SPECIAL

◆ sqrtK

sqrtK = []

◆ t

elseif Opt GP t = sqrtK

◆ theta

theta = mvnrnd(mu_theta,cov_theta)'

◆ TO

return function Yi Cao All rights reserved Redistribution and use in source and binary with or without are permitted provided that the following conditions are this list of conditions and the following disclaimer* Redistributions in binary form must reproduce the above copyright this list of conditions and the following disclaimer in the documentation and or other materials provided with the distribution THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED BUT NOT LIMITED TO

◆ TolCon

LSoptions TolCon = 1e-12

◆ TolFun

LSoptions TolFun = 1e-12

◆ TolX

LSoptions TolX = 1e-14

◆ ub

see Jones paper ub = ones(h1+h2,1) * log(sqrt(10^(3)))

◆ UseParallel

LSoptions UseParallel = 0

◆ v

Hypervolume v
Initial value:
=hypervolumemonte(P,r,N)
% Copyright (c) 2009

◆ V

return function Yi Cao All rights reserved Redistribution and use in source and binary with or without are permitted provided that the following conditions are this list of conditions and the following disclaimer* Redistributions in binary form must reproduce the above copyright this list of conditions and the following disclaimer in the documentation and or other materials provided with the distribution THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED BUT NOT LIMITED THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY OR CONSEQUENTIAL WHETHER IN STRICT OR EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE HYPERVOUME Hypervolume indicator as a measure of Pareto front estimate V
Initial value:
= HYPERVOLUME(P,R,N) returns an estimation of the hypervoulme (in
% percentage) dominated by the approximated Pareto front set P (n by d)
% and bounded by the reference point R (1 by d). The estimation is doen
% through N (default is 1000) uniformly distributed random points within
% the bounded hyper-cuboid.
%
% V = HYPERVOLUMN(P,R,C) uses the test points specified in C (N by d).
%
% See also: paretofront

◆ Variables

Scale Variables[xScaled, yScaled] = ScaleVariables(X,Y,lb,ub)

◆ W

else W = randn(nSpectralpoints,D) .* repmat(1./ell', nSpectralpoints, 1)

◆ WARRANTIES

return function Yi Cao All rights reserved Redistribution and use in source and binary with or without are permitted provided that the following conditions are this list of conditions and the following disclaimer* Redistributions in binary form must reproduce the above copyright this list of conditions and the following disclaimer in the documentation and or other materials provided with the distribution THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED WARRANTIES
r
upper bound of the data set r
Definition: Train_GP_and_return_hyperparameters.m:340
c
end c
Definition: Train_GP_and_return_hyperparameters.m:243
i
end Calculate covariance matrix and inverse of covariance matrix for i
Definition: Train_GP_and_return_hyperparameters.m:29
lb
Define bounds lb
Definition: Train_GP_and_return_hyperparameters.m:58
Opt
internal option for solver Opt
Definition: example_training_of_GP.m:48
zeros
size(X zeros()
X
lb+(ub-lb) .*X X
Definition: example_training_of_ANN.m:36
d
type of Martern else d
Definition: Train_GP_and_return_hyperparameters.m:104
Y
Scale inputs onto interval[lb, ub] Y
Definition: example_training_of_ANN.m:38
D
return function D
Definition: Predict_GP.m:113
P
Approximation of Pareto set P
Definition: Train_GP_and_return_hyperparameters.m:342
Ynew
scaled inputs Ynew
Definition: ScaleVariables.m:6
n
file Train_GP_and_return_hyperparameters m brief Trains a Gaussian processe and returns RWTH Aachen University n
Definition: Train_GP_and_return_hyperparameters.m:8
Xnew
id Xnew()
ub
see Jones paper ub
Definition: Train_GP_and_return_hyperparameters.m:59
V
return function Yi Cao All rights reserved Redistribution and use in source and binary with or without are permitted provided that the following conditions are this list of conditions and the following disclaimer *Redistributions in binary form must reproduce the above copyright this list of conditions and the following disclaimer in the documentation and or other materials provided with the distribution THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS AND ANY EXPRESS OR IMPLIED BUT NOT LIMITED THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY OR CONSEQUENTIAL WHETHER IN STRICT OR EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE HYPERVOUME Hypervolume indicator as a measure of Pareto front estimate V
Definition: Train_GP_and_return_hyperparameters.m:323
j
Training of GP for j
Definition: Train_GP_and_return_hyperparameters.m:24